On Groups with a Supercomplemented Subgroup

TL;DR

This paper investigates groups where every subgroup containing a specific primary cyclic subgroup has a complement, exploring their structural properties and implications for group theory.

Contribution

It introduces and analyzes a new class of groups characterized by supercomplemented subgroups, expanding understanding of subgroup complementarity.

Findings

Characterization of groups with supercomplemented subgroups

Conditions under which subgroups have complements

Structural properties of these groups

Abstract

Groups, in which every subgroup containing some fixed primary cyclic subgroup has a complement, are investigated.